_To the Editor._
Sir,--I send you a short and plain demonstration, that by travelling
eastward or westward round the globe at a given rate, (if it were
practicable to do so,) a man might experience a greater or lesser number
of days and nights, than if he were to remain still in the same spot.
This, I may venture to say, is a fact that very few people are aware of,
and few would believe, until it were proved.
As “this goodly frame, the earth,” turns round upon its own axis once in
twenty-four hours, and as the circumference of the globe is divided into
360 degrees, consequently every part of the globe’s surface must travel
round its axis at the rate of fifteen degrees in one hour; or, which is
the same thing, one degree in four minutes. Having premised this, we
will suppose that a man sets off at seven o’clock in the morning, just
as the sun rises above the horizon, and travels westward in the sun’s
ecliptic; one degree before it sets, he will have light four minutes
longer than if he were to remain at the place from whence he set out;
and his day, instead of being twelve hours long, (dividing the
twenty-four hours into twelve day and twelve night,) and closing at
seven o’clock, will be twelve hours and four minutes, and close at four
minutes past seven. He continues to travel in the same direction, and
with the same velocity, during the night, (for he must never rest,) and
that also will be four minutes longer than it would have been had he
remained at the place where the sun set till it again rose; because, as
he is travelling after the sun when it goes down, and from it as the
morning approaches, of course it will be longer in overtaking him: he
will be then two degrees from the starting place or goal, which you
please, for we intend to send him completely round the world, and the
sun will not rise the second morning till eight minutes past seven. His
travel continues at the same rate, and he again has the sun four minutes
longer, which does not set on the second day till twelve minutes past
seven: this closes the third day. The next morning the sun rises not
till sixteen minutes past seven; then he has travelled four degrees, and
his day and night have each been four minutes longer than if he had been
stationary. Now we will suppose another man to have gone from the same
place at the same moment, (_viz._ seven o’clock,) taking the opposite
direction. He travels east to meet the sun, and at the same rate of
travel as our westward bound wight. The sun will go down upon him four
minutes _sooner_ than if he had remained at the place from which he
started, and eight minutes sooner than upon the other man: his day will
close at fifty-six minutes past six. He goes on from the sun as it
sinks, and towards it as it rises, and he will have light four minutes
earlier than if he had stopped when the sun went down till it again
rose, eight minutes sooner than he would have seen it at the starting
post, and sixteen minutes sooner than the opposite traveller; this is at
the end of the second day. He travels on; light again deserts him four
minutes earlier, _viz._ at forty-eight minutes past six at the end of
three degrees, and the second morning the sun will rise at forty-four
minutes past six, sixteen minutes earlier than at the place he started
from, and thirty-two minutes earlier than with the other man, with whom
on the same morning it does not rise till sixteen minutes past seven. It
is plain therefore, that while the western traveller has only seen two
nights and two days, the eastern has enjoyed the same number of each,
and more than half an hour of another day; and it is equally plain that
if they continue to travel round the globe at the same rate of motion,
the eastern traveller will have more days and nights than the western;
those of the former being proportionally shorter than those of the
latter. The following shows the commencement and length of each day to
both travellers:--
WESTERN TRAVELLER’S EASTERN TRAVELLER’S
1st day begins 1st day begins
at 7 o’clock, at 7 o’clock,
morning. morning.
2 ------ 8 minutes past 7. 2 ------ 52 minutes past 6.
3 ------ 16 ------------ 7. 3 ------ 44 ------------ 6.
4 ------ 24 ------------ 7. 4 ------ 36 ------------ 6.
5 ------ 32 ------------ 7. 5 ------ 28 ------------ 6.
6 ------ 40 ------------ 7. 6 ------ 20 ------------ 6.
7 ------ 48 ------------ 7. 7 ------ 12 ------------ 6.
8 ------ 56 ------------ 7. 8 ------ 4 ------------ 6.
9 ------ 4 ------------ 8. 9 ------ 56 ------------ 5.
10 ------ 12 ------------ 8. 10 ------ 48 ------------ 5.
11 ------ 20 ------------ 8. 11 ------ 40 ------------ 5.
12 ------ 28 ------------ 8. 12 ------ 32 ------------ 5.
13 ------ 36 ------------ 8. 13 ------ 24 ------------ 5.
14 ------ 44 ------------ 8. 14 ------ 16 ------------ 5.
15 ------ 52 ------------ 8. 15 ------ 8 ------------ 5.
16 ------ -- ------------ 9. 30 degrees. 16 ------ -- ------------ 5.
17 ------ 8 ------------ 9. 17 ------ 52 ------------ 4.
18 ------ 16 ------------ 9. 18 ------ 44 ------------ 4.
19 ------ 24 ------------ 9. 19 ------ 36 ------------ 4.
20 ------ 32 ------------ 9. 20 ------ 28 ------------ 4.
21 ------ 40 ------------ 9. 21 ------ 20 ------------ 4.
22 ------ 48 ------------ 9. 22 ------ 12 ------------ 4.
23 ------ 56 ------------ 9. 23 ------ 4 ------------ 4.
24 ------ 4 ----------- 10. 24 ------ 56 ------------ 3.
25 ------ 12 ----------- 10. 25 ------ 48 ------------ 3.
26 ------ 20 ----------- 10. 26 ------ 40 ------------ 3.
27 ------ 28 ----------- 10. 27 ------ 32 ------------ 3.
28 ------ 36 ----------- 10. 28 ------ 24 ------------ 3.
29 ------ 44 ----------- 10. 29 ------ 16 ------------ 3.
30 ------ 52 ----------- 10. 30 ------ 8 ------------ 3.
31 ------ -- ----------- 11. 60 degrees. 31 ------ -- ------------ 3.
At the end of this degree, the sixtieth, the sun rises upon the eastern
traveller at three in the morning, he having had thirty days and thirty
nights. At the same degree it does not rise upon the western traveller
till eleven in the morning, he having had the same number of days and
nights. When, therefore, the morning of his thirty-first day is just
breaking, the eastern traveller has had the sun eight hours. They have
both then had an equal number of days and nights complete, but the
eastern will have had eight hours of another day more than the western.
Let us try it a little further. The
WESTERN TRAVELLER’S
32nd day will break at 8 min. past 11, morn.
33 16 11.
34 24 11.
35 32 11.
36 40 11.
37 48 11.
38 56 11.
39 4 12.
40 12 12.
41 20 12.
42 28 12.
43 36 12.
44 44 12.
45 52 12.
46 1 at noon, 90
degrees.
EASTERN TRAVELLER’S
32nd day will break at 52 min. past 2, morn.
33 44 2.
34 36 2.
35 28 2.
36 20 2.
37 12 2.
38 4 2.
39 56 1.
40 48 1.
41 40 1.
42 32 1.
43 24 1.
44 16 1.
45 8 1.
46 1. at noon, 90
degrees.
There appears to be two hours’ difference every fifteenth day.
WESTERN TRAVELLER’S
61st day will break at 3, P. M.
76 5
91 7.
EASTERN TRAVELLER’S
61st day will break at 11 at night.
76 9
91 7.
The men would now be together at the other side of the globe, and would
see the sun rise at the same moment, but he who had travelled eastward
would have seen a day and a night more than the other.
WESTERN TRAVELLER’S
106th day will break at 9, at night.
121 11.
136 1, morning.
151 3.
166 5.
181 7. 360 degrees.
EASTERN TRAVELLER’S
106th day will break at 5, P. M.
121 3.
136 1, noon.
151 11, A. M.
166 9.
181 7.
They will now be at the spot where they started from, the western
traveller having seen two days and two nights less than the
eastern.[516]